Calculus of Variations and Geometric Measure Theory

M. Caponi - A. Carbotti - F. Sapio

The viscoelastic paradox in a nonlinear Kelvin-Voigt type model of dynamic fracture

created by carbotti on 22 Oct 2023
modified on 09 Jul 2024


Published Paper

Inserted: 22 oct 2023
Last Updated: 9 jul 2024

Journal: Journal of Evolution Equations
Pages: 24
Year: 2024

ArXiv: 2310.14250 PDF


In this paper we consider a dynamic model of fracture for viscoelastic materials, in which the constitutive relation, involving the Cauchy stress and the strain tensors, is given in an implicit nonlinear form. We prove the existence of a solution to the associated viscoelastic dynamic system on a prescribed time-dependent cracked domain via a discretisation-in-time argument. Moreover, we show that such a solution satisfies an energy-dissipation balance in which the energy used to increase the crack does not appear. As a consequence, in analogy to the linear case this nonlinear model exhibits the so-called viscoelastic paradox.

Keywords: elastodynamics, monotone operators, Energy-dissipation balance, Dynamic fracture, cracking domains, nonlinear viscoelasticity, viscoelastic paradox